Tromino

A tromino or triomino is a polyomino of size 3, that is, a polygon in the plane made of three equal-sized squares connected edge-to-edge.

When rotations are also considered distinct, there are six fixed trominoes: two I and four L shapes.

In this context, the L-tromino is called a chair, and its tiling by recursive subdivision into four smaller L-trominos is called the chair tiling.

[5] Motivated by the mutilated chessboard problem, Solomon W. Golomb used this tiling as the basis for what has become known as Golomb's tromino theorem: if any square is removed from a 2n × 2n chessboard, the remaining board can be completely covered with L-trominoes.

To prove this by mathematical induction, partition the board into a quarter-board of size 2n−1 × 2n−1 that contains the removed square, and a large tromino formed by the other three quarter-boards.